I appear to be having the same issue as five years ago: Wired headset microphone not recognised - #5 by Loki
Liberty Phone Crimson: I either plug in or bluetooth in a wired/wireless headset and the Output regesters fine and auto-connects, but there is no corresponding Input, which means I have to use the handset’s mic. This is for making calls. Ideas?
That is an older issue which I believe has been resolved. I am able to plug in wired earbuds w/ mic and have it detect. The important thing is to remember to flip your hardware kill switch to where the microphone is powered on before you plug it in.
As for connection over Bluetooth, I have never really tested it out, so I am not sure of any tricks. Maybe make sure the sound profile is set to HFP (hands free profile) after you have connected the headset through Bluetooth.
Maybe actually HSP (HeadSet Profile)?